{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Introduction\n",
    "<p>This notebook is a tutorial on the very powerful and elegent ensemble learning method known as Gradient Boosted Trees. This tutorial is organized as follows:<br>\n",
    "<ul>\n",
    "    <li>Theory, Derivation and Motivation</li>\n",
    "    <li>Simple illustration of fitting and model selection on simulated data</li>\n",
    "    <li>Comparison between GBT and other popular non-linear techniques on simulated data</li>\n",
    "    <li>References</li>\n",
    "</ul><br>\n",
    "There are many resources and tutorials available for learning about Gradient Boosted Trees. In an effort to attempt an original contribution, my goal here is to provide a comprehensive overview of the relevant theory as well as serve as a practical guide to implementing in Python. I have found that most tutorials cover one or the other. Additionally, I find that that vizualing a classifier's behavior is a great way to fully understanding what the theory attempts to express. Many of the vizualiztions below serve to illustrate the underlying mechanics of the method.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Theory, Algorithm and Derivation\n",
    "<p>The following sections go into increasing technical depth about GBTs. The first part introduces the basic functional form of a GBT. This should be the minimum that one learns to have at least a baseline understanding of the method. Next is presented the algorithm. Understanding the training algorithm leads to a nice intuitve understanding as to why the method works so well. It also helps to solidify the roles of the different hyperparameters. The last section derives the GBT algorithm. Knowing this is a nice way to geek out. \n",
    "\n",
    "\n",
    "</p>\n",
    "\n",
    "###Basic Functional Form\n",
    "<p>A Gradient Boosted Tree classifier can be thought of as a linear classifier over features that are learned specifically on your training data. The GBT classifier has the following functional form:\n",
    "\n",
    "<center>$P(Y|X) = [1 + e^{-F^m(X)}]^{-1}$</center><br>where,<br>\n",
    "\n",
    "<center>$F^m(X) = \\sum\\limits_{j=1}^{m}\\gamma_j * T(X;\\Theta_j)$</center><br><br>\n",
    "\n",
    "Notice that this functional form is nearly identical to standard Logistic Regression. They are similar in using the inverse logit to convert a linear function of $X$ to a probability. They are different in how the linear function is built. Additionally, each \"feature\" $T(X;\\Theta_j)$ in this linear function is a Decision Tree learned over some subpace of the original data. The power of GBTs is in how it learns and weights these component trees in such a way that it can approximate any non-linear function between $X$ and $Y$. \n",
    "</p>\n",
    "\n",
    "###Generic Algorithm\n",
    "<p>\n",
    "<ul>\n",
    "<li>Initialize the model with a constant value: $F^0(X) = \\underset{\\gamma} {\\mathrm{argmin}} \\: \\mathbb{L}(\\gamma,\\, Y)$</li>\n",
    "\n",
    "<li>For m=1 to M:</li>\n",
    "<ul>\n",
    "\n",
    "<li>Compute the gradient (pseudo residual) $r_{im}=-\\nabla_f \\, \\mathbb{L}(F^{m-1}(x_i))$ for each data point. </li>\n",
    "<li>Use least squares to fit a tree $T(X;\\Theta_m)$ to the residuals $r_{im}$. Each tree can be defined by $J$ regions, each denoted $R_{jm}$.</li>\n",
    "\n",
    "<li>Using each $R_{jm}$, identify the optimal step size using \n",
    "$\\gamma_{jm} =\\underset{\\gamma} {\\mathrm{argmin}} \\: \\sum\\limits_{x_i \\in R_{jm}} \\mathbb{L}(F^{m-1}(x_i) + \\gamma, y_i)$</li>\n",
    "\n",
    "<li>Update the base function: $F^m(X) = F^{m-1}(X) + +\\nu \\, \\sum\\limits_{j=1}^J\\gamma_{jm} \\, I(X \\in R_{jm})$</li>\n",
    "</ul>\n",
    "\n",
    "</ul>\n",
    "\n",
    "\n",
    "\n",
    "</p>\n",
    "\n",
    "\n",
    "\n",
    "###Derivation of Learning Algorithm\n",
    "<p>Learning a GBT classifier fits within the ERM framework. We showed above that the basic functional form of a GBT is $F^m(X)=\\sum\\limits_{j=1}^m f_j(X)$. To find the optimal $F^m(X)$, we define the following optimization problem:<br><br>\n",
    "\n",
    "<center>$F^{*}(X)= \\underset{\\mathbb{F}} {\\mathrm{argmin}} \\: \\mathbb{L}(F^m(X),\\, Y)$</center><br>\n",
    "\n",
    "\n",
    "\n",
    "For classification, we will use Log-Loss as our objective function:<br><br>\n",
    "<center>$\\mathbb{L}(F^m(X),\\, Y) =-\\sum\\limits_{i=1}^n y_i\\,ln\\,(p_i)+(1-y_i)\\,ln\\,(1-p_i)$</center><br><br>\n",
    "where $p(x_i)$ is defined using the inverse logit function. We can make this problem more palatable by solving it in a greedy, stagewise manner. If we have solved up to $F^{m-1}(X)$, we update the problem by finding the next best function $f(X)$ to add to $F^{m-1}(X)$. This leads to the following:<br><br>\n",
    "\n",
    "\n",
    "<center>$F^{m}(X)= F^{m-1}(X) \\:+\\: \\underset{f} {\\mathrm{argmin}} \\: \\mathbb{L}(F^{m-1}(X) \\,+\\, f(X),\\, Y)$</center><br><br>\n",
    "\n",
    "In lieu of solving for the optimal $f(X)$ directly, we employ a steepest descent line search to move closer to the optimal loss. This can be expressed as:<br><br>\n",
    "\n",
    "<center>$F^m(X) = F^{m-1}(X) - \\gamma_m * \\nabla_f \\, \\mathbb{L}(F^{m-1}(X) \\,+\\, f(X))$</center><br><br>\n",
    "\n",
    "Where the gradient $\\nabla_f \\mathbb{L}$ is with respect to the function $f(X)$. If we know the gradient exactly, we can compute the best step direction by solving:<br><br>\n",
    "\n",
    "<center>$\\gamma^* = \\underset{\\gamma} {\\mathrm{argmin}} \\: \\mathbb{L}(F^{m-1}(X) \\,-\\, \\gamma \\nabla_f \\mathbb{L})$</center><br><br>\n",
    "\n",
    "In order to better generalize, we want to approximate the gradient with a function that is highly correlated to it, but is defined over $X$ values not in the training data. Any family of functions is suitable, but a popular choice is decision tree. So before solving the line search, we first find a tree $T(X;\\Theta_m)$ that best approximates the negative gradient at each boosting step. This can be expressed as:<br><br>\n",
    "\n",
    "<center>$T(X;\\Theta_m) = \\underset{\\Theta}{\\mathrm{argmin}} (-\\nabla_f \\, \\mathbb{L} - T(X;\\Theta))^2$</center><br><br>\n",
    "\n",
    "So after this step is done, we do the line search using the fitted tree and not the actual gradient. Our final optimzation step is then:<br><br>\n",
    "\n",
    "<center>$\\gamma_m = \\underset{\\gamma} {\\mathrm{argmin}} \\: \\mathbb{L}(F^{m-1}(X) \\,-\\, \\gamma T(X;\\Theta_m))$</center><br><br>\n",
    "\n",
    "With this we update our base function:\n",
    "\n",
    "<center>$F^m(X) = F^{m-1}(X) + \\gamma_m \\, T(X;\\Theta_m)$</center><br><br>\n",
    "\n",
    "So to recap the above, at each step we do the following:<br>\n",
    "<ul>\n",
    "<li>Compute the gradient $\\nabla_f \\, \\mathbb{L}(F^{m-1}(X) \\,+\\, f(X))$ over the data </li>\n",
    "<li>Use least squares to fit a tree $T(X;\\Theta_m)$ to the gradient.</li>\n",
    "<li>Using $T(X;\\Theta_m)$, identify the optimal step size $\\gamma_m$</li>\n",
    "<li>Update the base function.</li>\n",
    "</ul>\n",
    "</p>\n",
    "\n",
    "###Fitting Residuals\n",
    "<p>In the line search steps above, we used a decision tree to make a best least squares approximation to the gradient of the loss function. This is well motivated mathematically, but there is also a very intuitive interpretation to this. The gradient of $\\mathbb{L}$ with respect to $f(X)$ is essentially the residual between $Y$ and $F^{m-1}(X)$. So for ordinary least squares, the gradient is $\\nabla_f \\mathbb{L} = Y-F^{m-1}(X)$, and for classification, we have $\\nabla_f \\mathbb{L} = Y-p(X)$.<br><br>\n",
    "When we think about the tree fitting step above, what we are really doing is fitting a tree to the residuals of the $(m-1)th$ step. Each boosting step then emphasizes the data points where predictions are the most incorrect.\n",
    "</p>\n",
    "\n",
    "###Regularization\n",
    "\n",
    "<p>As with any prediction model, we need to take care to avoid over-fitting. This is done by adding a dampening constant to the estimate of $F^m(X)$. Specifically, we introducte $\\nu$, such that:<br><br>\n",
    "<center>$F^m(X) = F^{m-1}(X) + \\nu \\, \\gamma_m \\, T(X;\\Theta_m)$</center><br><br>\n",
    "The value of $\\nu$ is usually find with a grid-search and cross-validation procedure. \n",
    "\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "##A Simulation Study\n",
    "\n",
    "<p>\n",
    "A good way to understand gradient boosting is to work with a small dataset in which we know the true data generating function $F^*(X)$. For this example we have $X$ uniformly distributed in the unit square, and $Y$ is distributed as such:<br><br>\n",
    "\n",
    "<center>$Y = I((X_1 - 0.5)^2 + (X_2 - 0.5)^2 + \\epsilon < \\delta)$</center><br><br>\n",
    "Here $I(*)$ is the indicator function that returns $1$ if the expression is true, and $\\epsilon \\sim N(0,\\sigma^2)$. The additive gaussian noise determines how cleanly any decision function can separate the classes.<br><br>\n",
    "\n",
    "For this simulation, we will first generate training and testing sets, and then do several experiments to illustrate the boosting procedure.\n",
    "<p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
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   "outputs": [
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eQR0WWnxFtQseDM4n24BfUhlqOxeBZNLSOnabtOD2sqvDSikoNDMhSyvnYXra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\nD/xAPJjuAw888MAPxIPpPvDAAw/8QPw/FqX4v74rFicAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10969af50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Generate random data with classes separated by a circle with some gaussian noise\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "n=10000\n",
    "circle = [(0.5, 0.5), 0.25]\n",
    "sig = 0.1\n",
    "\n",
    "X1 = np.random.random(n)\n",
    "X2 = np.random.random(n)\n",
    "Y = 1*(((X1 - circle[0][0])**2 + (X2 - circle[0][1])**2 + np.random.randn(n)*sig) < circle[1]**2)\n",
    "X = pd.DataFrame({'X1':X1, 'X2':X2})\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "plt.plot(X1[(Y==0)], X2[(Y==0)], 'b.', markersize=3)\n",
    "plt.plot(X1[(Y==1)], X2[(Y==1)], 'r.', markersize=3)\n",
    "ax.axes.get_xaxis().set_visible(False)\n",
    "ax.axes.get_yaxis().set_visible(False)\n",
    "plt.title('Simulated 2-Class Data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>\n",
    "Now let's compare training and test error as a function of the # of estimators. Note that since this data has only 2 features, we only need a max_depth of 2 for the decision trees to express any interactions that may exist in the data. \n",
    "<p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GradientBoostingClassifier(init=None, learning_rate=0.1, loss='deviance',\n",
       "              max_depth=2, max_features=None, min_samples_leaf=1,\n",
       "              min_samples_split=2, n_estimators=1000, random_state=None,\n",
       "              subsample=1.0, verbose=0)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import GradientBoostingClassifier\n",
    "from sklearn.metrics import confusion_matrix,roc_auc_score\n",
    "\n",
    "split_ind = 0.7 * len(Y)\n",
    "\n",
    "X_train = X[:split_ind]\n",
    "Y_train = Y[:split_ind]\n",
    "X_test = X[split_ind:]\n",
    "Y_test = Y[split_ind:]\n",
    "\n",
    "n_est_lim = 1000\n",
    "gbc = GradientBoostingClassifier(n_estimators = n_est_lim, max_depth = 2)\n",
    "gbc.fit(X_train, Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now lets plot using the staged_predict_proba method for GradientBoostingClassifier. This method returns a generator that when called can give us the predictions at each stage of the model building process. This will let us see how training and test error (Log-Loss) evolve as we grow the model.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x114a41690>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mRMLq6IHUQQMAAMAn+VyATkiQjoanSE1OQAQAAAB8hc8F6JQU6WBgCjPQAAAA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\nAl/wdqpsGs9gAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114a8b9d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "from pylab import rcParams\n",
    "rcParams['figure.figsize'] = 12, 5\n",
    "\n",
    "\n",
    "def LogLossP(Pt, Yt):\n",
    "    return -1*((Yt==1)*np.log(Pt)+(Yt==0)*np.log(1-Pt)).mean()\n",
    "\n",
    "p_train = gbc.staged_predict_proba(X_train)\n",
    "p_test = gbc.staged_predict_proba(X_test)\n",
    "\n",
    "ll_train = []\n",
    "ll_test = []\n",
    "\n",
    "for p in p_train:\n",
    "    ll_train.append(LogLossP(p[:, 1], Y_train))\n",
    "    \n",
    "for p in p_test:\n",
    "    ll_test.append(LogLossP(p[:, 1], Y_test))\n",
    "    \n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "plot(np.arange(1, n_est_lim + 1), ll_train, 'b-', label='Train')\n",
    "plot(np.arange(1, n_est_lim + 1), ll_test, 'r-', label='Test')\n",
    "plt.title('Training and Testing Error as a Function of N-Estimators')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>We can see above the typical pattern as we make a classifier more complex. In this case, the power of the classifier improves dramatically in the first few dozen iterations. After that, we see a continual improvement in Training error, but of course at the cost of good Test error. Notice though the cost of overfitting is fairly mild here. So having too many iterations is better than having too few. <br><br>\n",
    "\n",
    "Next let's actually visualize what the classifier is doing. Remember that our function here is an additive function of weighted trees.<br><br>\n",
    "\n",
    "<center>$F^m(X) = \\sum\\limits_{j=1}^{m}\\gamma_j * T(X;\\Theta_j)$</center><br><br>\n",
    "\n",
    "The first thing we can do to better understand this function is plot the decision boundaries of the first $k$ terms. The GradientBoostedClassifier object has an attribute estimators_ that is a list with each element being a component tree. We can thus plot the decision surface of each tree. Note too that the base function is a regression tree, since we are predicting residuals at each step and not the actual label. \n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vUyzKLnKbDUa6WtLIcGik8GOza+8zugTQL/OUtEu5FgNtqV2yptAyoY0LYgFj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\nhGc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km6XnQ7+D63NHYG59RXyuU2JIc264IkF6pvoPL6rffSlr5UcsaZDKO1GE9rwPZeIP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\nFBQUdBr/P3yLfPDuXp4TAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115a2e650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Specify the plot grid\n",
    "\n",
    "from pylab import rcParams\n",
    "rcParams['figure.figsize'] = 12, 12\n",
    "\n",
    "plot_step = 0.02\n",
    "x_min, x_max = X['X1'].min(), X['X1'].max()\n",
    "y_min, y_max = X['X2'].min(), X['X2'].max()\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, plot_step),np.arange(y_min, y_max, plot_step))\n",
    "\n",
    "#Now plot\n",
    "fig = plt.figure()\n",
    "\n",
    "for i in range(1,10):\n",
    "    ax = fig.add_subplot(3, 3, i)\n",
    "    Z = gbc.estimators_[i][0].predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "    cs = plt.contourf(xx, yy, Z, cmap=plt.cm.cool)\n",
    "    plt.plot(X['X1'][(Y==1)], X['X2'][(Y==1)], 'r.', markersize = 2)\n",
    "    ax.axes.get_xaxis().set_visible(False)\n",
    "    ax.axes.get_yaxis().set_visible(False)\n",
    "    plt.title('{}th Tree'.format(i))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now let's plot the decision surface of the classifier. I.e., we will look at:<br><br>\n",
    "<center>$P^m(X) = [1+e^{-F^m(X)}]^{-1}$</center>\n",
    "for different values of m.\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kncDodGhtjZuhlsAKwBavftbl52SzpDvKSvDNDj+FVYJqaqLbK9VQmM3RUTeXxTGsABzH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\nAEBoYLACAAAAAIDQ/D8a8uOihgWg8AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f35410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Predict on the grid points, which were defined above\n",
    "p_gen = gbc.staged_predict_proba(np.c_[xx.ravel(), yy.ravel()])\n",
    "p_test = gbc.staged_predict_proba(X_test)\n",
    "\n",
    "#Now plot\n",
    "fig = plt.figure()\n",
    "\n",
    "k = 3\n",
    "\n",
    "ms = np.arange(1, k*k + 1)**3\n",
    "\n",
    "cnt = 0\n",
    "for i in range(1, k*k + 1):\n",
    "    while (cnt < ms[i-1]):\n",
    "        Z = p_gen.next()[:, 1]\n",
    "        P = p_test.next()[:, 1]\n",
    "        LL = LogLossP(P, Y_test)\n",
    "        cnt += 1\n",
    "        \n",
    "    Z = Z.reshape(xx.shape)\n",
    "    ax = fig.add_subplot(k, k, i)\n",
    "    cs = plt.contourf(xx, yy, Z, cmap=plt.cm.cool)\n",
    "    ax.axes.get_xaxis().set_visible(False)\n",
    "    ax.axes.get_yaxis().set_visible(False)\n",
    "    plt.title('iter {}, LL={}'.format(cnt, round(LL,3)))\n",
    "\n",
    "   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>In the above plots we can get a good sense of the bias-variance tradeoff of the GBT classifier. With a few iterations, we get a large box in the middle with very little curvature around it. As we add more boosts, we can see how the decision surface gets more spherical. With this also increase we also see the prediction region becoming more speckled with predictions of the negative class (blue). This is the GBT fitting noisy points within the circle. We can see how the log-loss decreases as we add more trees, but eventually it goes up again. Overall though, on this data, it is better to err on more tree than fewer. This method is more robust to high variance than to high bias.\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##A Simulation Bakeoff\n",
    "\n",
    "<p>In this section we'll compare Gradient Boosting to two other non-linear methods: Random Forests and SVM with Radial Basis Kernel. We'll first generate 2 datasets that have highly non-linear decision boundaries. The following two data sets are generated from the same underlying geometry, only one has a lot of noise added to it.\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10ab37e10>]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from course_utils import *\n",
    "\n",
    "noisy_train = happyClass(0.015, 2000)\n",
    "clean_train = happyClass(0.0001, 2000)    \n",
    "noisy_test = happyClass(0.015, 5000)\n",
    "clean_test = happyClass(0.0001, 5000)    \n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.title('Noisy Face')\n",
    "plt.plot(noisy_test.X1[(noisy_test.Y==0)], noisy_test.X2[(noisy_test.Y==0)], 'b.')\n",
    "plt.plot(noisy_test.X1[(noisy_test.Y==1)], noisy_test.X2[(noisy_test.Y==1)], 'r.')\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.title('Clean Face')\n",
    "plt.plot(clean_test.X1[(clean_test.Y==0)], clean_test.X2[(clean_test.Y==0)], 'b.')\n",
    "plt.plot(clean_test.X1[(clean_test.Y==1)], clean_test.X2[(clean_test.Y==1)], 'r.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p> Next we'll do the bakeoff. The goal here is to see how the above algorithms perform on the above simulated data. We also want to compare the decision surfaces so that we can pull a bit of geometric intuition about how each classifier operates. For each classifier type in this bakeoff we'll use SKLearn's GridsearchCV to perform cross-validation to choose a set of optimal hyper-parameters.\n",
    "\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=10000, cache_size=200, class_weight=None, coef0=0.0, degree=3, gamma=1,\n",
       "  kernel='rbf', max_iter=-1, probability=True, random_state=None,\n",
       "  shrinking=True, tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.grid_search import GridSearchCV\n",
    "from sklearn.ensemble import GradientBoostingClassifier\n",
    "from sklearn.ensemble  import RandomForestClassifier\n",
    "from sklearn.cross_validation import KFold\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "boost_grid = {'n_estimators':[20, 50, 100, 500, 1000]}\n",
    "rf_grid = {'n_estimators':[20, 50, 100, 500, 1000], 'max_features':[1, 2]}\n",
    "svm_grid = {'C': [1000, 10000, 100000], 'gamma': [100, 10, 1, 0.1], 'kernel': ['rbf']}\n",
    "\n",
    "\n",
    "#We define a KFold object so that all tests get the same folds\n",
    "kf = KFold(noisy_train.shape[0], n_folds=5)\n",
    "\n",
    "boost_cv = GridSearchCV(GradientBoostingClassifier(), boost_grid, cv = kf, scoring = 'roc_auc')\n",
    "boost_cv.fit(noisy_train.drop('Y', 1), noisy_train.Y)\n",
    "\n",
    "rf_cv = GridSearchCV(RandomForestClassifier(), rf_grid, cv = kf, scoring = 'roc_auc')\n",
    "rf_cv.fit(noisy_train.drop('Y', 1), noisy_train.Y)\n",
    "\n",
    "svm_cv = GridSearchCV(SVC(), svm_grid, cv = kf, scoring = 'roc_auc')\n",
    "svm_cv.fit(noisy_train.drop('Y', 1), noisy_train.Y)\n",
    "#We need these steps to get the prob estimate off of the SVM\n",
    "svc = svm_cv.best_estimator_\n",
    "svc.probability = True\n",
    "svc.fit(noisy_train.drop('Y', 1), noisy_train.Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p>Now let's plot these\n",
    "\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zkt/GDx06VP07JydH8zk7O9tw3gwfPhzt7e3qv6qqKnzyyScR857oT2Pg53kwGFSfg/49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\n57tsM+gKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac431d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plotZgen(clf, dat, pc, t, fig):\n",
    "    '''\n",
    "    This plots a 2d decision boundary given a trained classifier\n",
    "    Note the data must have two fields X1 and X2 to work\n",
    "    '''\n",
    "    plot_step = 0.02\n",
    "    x_min, x_max = dat['X1'].min(), dat['X1'].max()\n",
    "    y_min, y_max = dat['X2'].min(), dat['X2'].max()\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, plot_step),np.arange(y_min, y_max, plot_step))\n",
    "    Z = clf.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1]\n",
    "    Z = Z.reshape(xx.shape)\n",
    "    ax = fig.add_subplot(pc[0], pc[1], pc[2])\n",
    "    cs = plt.contourf(xx, yy, Z, cmap=plt.cm.cool)\n",
    "    plt.plot(dat['X1'][(dat.Y==1)], dat['X2'][(noisy_test.Y==1)], 'r.', markersize = 2)\n",
    "    plt.title(t)\n",
    "    ax.axes.get_xaxis().set_visible(False)\n",
    "    ax.axes.get_yaxis().set_visible(False)\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "plotZgen(boost_cv, noisy_test, (1, 3, 1), 'Gradient Boosted Tree', fig)\n",
    "plotZgen(rf_cv, noisy_test, (1, 3, 2), 'Random Forest', fig)\n",
    "plotZgen(svc, noisy_test, (1, 3, 3), 'SVM - Guassian Kernel', fig)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#References\n",
    "<p>The following list of references are recommended for a complete review of both the implementation and theory of Gradient Boosted Trees.<br>\n",
    "<ul>\n",
    "    <li><a href=\"http://en.wikipedia.org/wiki/Gradient_boosting\">Sklearn's GBT Documentation</a></li>\n",
    "    <li><a href=\"http://scikit-learn.org/stable/modules/ensemble.html\">Wikipedia</a></li>\n",
    "\n",
    "\n",
    "</ul>\n",
    "\n",
    "\n",
    "</p>"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
